Anthem Blue Cross and Blue Shield Maine Customer Service Hours 8:00 a.m. – 5:30 p.m. (EST) Monday, Tuesday, Wednesday & Friday 9:00 a.m. – 5:30 p.m. Thursday General Information 800-722-0203 Anthem Blue Cross and Blue Shield New Hampshire Customer Service Hours 8:00 a.m. – 5:30 p.m. (EST) Monday, Tuesday, Wednesday & Friday 9:00 a.m. – 5:30 p.m. Thursday General Information 800-852-3316 Send Claims To PO Box 105557 Atlanta, GA 30348-5557